A General EXCEL Solution for LTPD Type Sampling Plans David C. Trindade, Ph.D. Sun Microsystems David Meade AMD 1999 Joint Statistical Meetings Baltimore, MD
Mar 29, 2015
A General EXCEL Solution for LTPD Type Sampling Plans
David C. Trindade, Ph.D.Sun Microsystems
David MeadeAMD
1999 Joint Statistical Meetings Baltimore, MD
Lot Acceptance Sampling
• Assume single random sample of size n from a process or a very large lot.
• Binomial distribution is appropriate.
• Refer to as type B sampling.
Sampling Plan
• Specifies – the sample size n– the acceptance number c
• An operating characteristic (OC) curve shows the probability of lot acceptance for a given level of incoming lot percent defective p
n = 50 c = 3
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
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1.00
0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%
Lot Percent Defective
Pro
bab
ility
of
Acc
ep
tan
ceOC Curve
LTPD Plans
• The quality level at 10% probability of acceptance (consumer’s risk) is called the LTPD.
• This rejectable quality level (RQL) is highest percent defective (poorest quality) tolerable in a small percentage of product.
• Borderline of distinction between a satisfactory lot and an unsatisfactory one.
• LTPD plans are used for many product qualification plans to assure consumer protection.
Common Sampling Problem in Industry
• There are constraints on sample size based on limited time, money, or other resources.
• There is often the need to adjust sample size and corresponding acceptance number while holding LTPD constant.
LTPD Tables
Limitations of Tables
• LTPD values restricted to only those listed.
• There are finite ranges of sample sizes and acceptance numbers.
Example Case
• Reliability qualification plan for integrated circuits calls for stressing a sample of 300 units for 1000 hours. Pass requirement is no more than three failures.
• Early samples are precious, costing approximately $10,000 each and are needed for other evaluations.
• How can the engineer reduce the sample size and allowed failures while holding the LTPD constant?
Approaches by Engineer
• First, the LTPD value must be determined.
• Then, LTPD tables may be consulted to see if n = 300 and c = 3 are tabulated.
• Approximation may be necessary:– Checking LTPD table, we see n = 333 and c = 3
for LTPD = 2%.– For c = 1, LTPD = 2%, we need n = 195.
Graphical Techniques*
*Applied Reliability, 2nd ed., P. Tobias and D. Trindade
Graphical Results
• For n = 300, c = 3, LTPD = 2.2%.
• For LTPD = 2.2%, c = 1, n ~ 180.
There is a limitation in these graphs to
only c = 0, 1, 2, or 3.
EXCEL Solution (Add-In)
Find LTPD for Given Sampling Plan
Find LTPD for a Given sampling Plan: Output
Find Alternative LTPD Sampling Plan
Find Alternative Sampling Plan: Output
Find Sample Size for Given c
Find Sample Size for Given c: Output
Final Comments
• Description and theory presented in paper.
• LTPD add-in and paper available for download from www.trindade.com/LTPD.html
• Questions to:– [email protected]– [email protected] (VB programming)